The Economic Value of Targeting Aging

Analysis https://doi.org/10.1038/s43587-021-00080-0

The economic value of targeting aging

Andrew J. Scott 1 ✉ , Martin Ellison 2 and David A. Sinclair 3

Developments in life expectancy and the growing emphasis on biological and ‘healthy’ aging raise a number of important questions for health scientists and economists alike. Is it preferable to make lives healthier by compressing morbidity, or longer by extending life? What are the gains from targeting aging itself compared to efforts to eradicate specific diseases? Here we analyze existing data to evaluate the economic value of increases in life expectancy, improvements in health and treatments that target aging. We show that a compression of morbidity that improves health is more valuable than further increases in life expectancy, and that targeting aging offers potentially larger economic gains than eradicating individual diseases. We show that a slowdown in aging that increases life expectancy by 1 year is worth US$38 trillion, and by 10 years, US$367 trillion. Ultimately, the more progress that is made in improving how we age, the greater the value of further improvements.

ife expectancy (LE) has increased dramatically over the past rates, retirement age, and knowledge of remaining LE and likely 150 years1, although not all of the years gained are healthy. future health. Changes in health or longevity lead to changes in these LAnalysis of the Global Burden of Disease dataset2 suggests that economic decisions, enabling us to estimate an individual’s willing- the proportion of life in good health has remained broadly con- ness to pay (WTP) for these improvements. WTP is measured in US stant, implying increasing years in poor health. Furthermore, the dollars and reflects the increase in VSL induced by improvements in disease burden is shifting towards chronic non-communicable dis- health and longevity. VSL is the sum of the value of each remaining eases, estimated to have caused 72.3% of deaths in the United States year of life, discounted to the present day and weighted by the sur- in 2016. The result is “a substantial part of life, and certainly most vival rate. As the value of each year of life depends on health, con- deaths, now occur in a period in the lifespan when the risk for frailty sumption and leisure, the VSL incorporates both the quantity and and disability increases exponentially.”3 As a consequence, there is quality of expected life remaining. Importantly, this means that the a growing emphasis on ‘healthy aging’ and an emerging body of VSL is higher than an individual’s lifetime income; life is valuable research focusing on the biology of aging (see refs. 4,5). According in its own right because individuals value time, health and leisure. to another paper, “this era marks an inflection point, not only in The demographic data underpinning our analysis are: (1) a sur- aging research but also for all biological research that affects the vival function12, in which mortality risk increases exponentially human healthspan.”6 with age; (2) a health deficit function13, which also increases expo- These developments pose a number of important questions. Is it nentially with age; and (3) the 2017 population structure and birth preferable to make lives healthier by compressing morbidity, or lon- rates from the US Census Bureau. In our baseline calculations, LE ger by extending life? What are the gains from targeting aging itself, and healthy life expectancy (HLE) at birth are 78.9 and 68.5 years, with its potential to make lives both healthier and longer? How does respectively, based on current US data. Following ref. 14, we set the the value of treating aging compare to eradicating specific diseases? average VSL of an adult aged between 25 and 65 years to US$11.5 How will the economic value of these gains evolve over time? To million. Although our dollar WTP values are sensitive to the precise answer these questions, we take an economic rather than biologi- calibration of our model, the relative importance of different treat- cal perspective. Specifically, we use the value of statistical life (VSL) ments for aging is not. methodology to place a monetary value on the gains from longer life, better health, and changes in the rate at which we age7–9. Life extension (the Struldbrugg case). We first focus on improv- VSL models have two distinct advantages for our purposes. First, ing LE which, with reference to Gulliver’s Travels15, we refer to as they are already used by government agencies to evaluate different the Struldbrugg case. Struldbruggs, both male and female, are policy measures and treatments, for example10,11. Second, as our born immortal but age normally, so live in continuously worsen- model is based around optimizing economic agents, we can calcu- ing health. In our simulations, we achieve this by reducing the rate late not only the current gains from targeting aging but also how at which mortality increases with age while holding unchanged the these gains will evolve in response to potential future changes in rate at which health declines. The result is an expansion of morbid- health and LE. The results reveal a distinctive feature of age-target- ity such that the ratio of HLE to LE deteriorates. ing treatments. Interactions between health, longevity, economic The WTP for LE increases depends on which years benefit from decisions and demographics create a virtuous circle, such that the lower mortality. To provide consistency across simulations, we more successful society is in improving how we age, the greater the assume mortality is subject to a compensating effect16 whereby it economic value of further improvements. reaches a rate M at age T. Under this specification, there are two ways to extend LE. The first is to rectangularize the survival func- Results tion such that M and T are kept constant but mortality falls at all Our economic model is based on that in ref. 8 and calibrated to cur- ages less than T while rising more rapidly at T (Fig. 1, blue survival rent US data. In the model, individuals make choices about con- function). The second involves increasing lifespan, such that mor- sumption, hours worked and leisure based on wage rates, interest tality reaches M at higher values of T. In this case, survival rates

1Department of Economics, London Business School, London, UK. 2Department of Economics, University of Oxford, Oxford, UK. 3Harvard Medical School, Boston, MA, USA. ✉e-mail: [email protected]

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0.00 147101316192225283134374043464952555861646770737679828588919497100 103106 109112115118 121 Age (years)

Baseline Compression through rectangularization Lifespan improvement

Fig. 1 | Survival functions under rectangularization and improvement in lifespan. Three different survival functions (probability of surviving from birth to different ages). Baseline is a standard Gompertz–Makeham survival function calibrated to 2019 US data. The rectangularization curve shows a survival function in which improvements in LE are achieved through compressing morbidity. The lifespan improvement curve shows a survival function in which improvements arise through elongation of the aging process.

Table 1 | WTP for 1-year increases in remaining LE (the Struldbrugg case) Age at which WTP is calculated (years) 0 20 40 60 80 R L R L R L R L R L First 118.1 96.5 171.0 141.5 232.0 199.4 285.6 257.7 312.2 288.1 Second 114.1 93.4 165.5 137.1 226.1 193.2 279.7 250.0 304.4 278.1 Third 110.0 90.4 160.1 132.7 220.0 187.2 273.8 242.1 298.0 268.5 Fourth 105.9 87.5 154.5 128.4 213.8 181.3 267.7 234.6 292.0 259.4 Fifth 101.8 84.6 148.9 124.3 207.4 175.6 261.5 227.4 286.0 250.7 Tenth 81.8 71.5 120.8 105.0 173.0 149.1 226.2 193.8 225.3 212.2 Twentieth 50.3 74.0 105.9 139.3 152.7 Thirtieth 35.0 51.6 74.3 98.8 109.5

WTP for the first, second and further 1-year increases in remaining LE at ages 0, 20, 40, 60 and 80 years. The LE remaining at these ages in the baseline simulation is 78.9, 59.0, 39.5, 21.7 and 8.4 years. Some values are missing because there is an upper limit to how much LE can be extended through rectangularization. Values are given in US$1,000. L, improvements in lifespan T; R, rectangularization.

decline more slowly, increasing the probability of living beyond T 79.9 years via rectangularization is US$118,100, the WTP at age 60 (Fig. 1, yellow survival function). for the first 1-year increase in remaining LE from 21.7 to 22.7 years Table 1 shows the WTP for increases of 1 year in remaining LE through lifespan improvement is US$257,700. The subsequent rows through rectangularization versus improvements in lifespan, at ages (Second, Third, and so on) show the WTP for additional 1-year 0, 20, 40, 60 and 80 years. The first row is the WTP for the initial increases, so in the row starting ‘Tenth’, the WTP at age 20 shows an (First) 1-year increase from our baseline; for example, the WTP at increase in remaining LE from 68.0 to 69.0 years, since by the tenth birth for the initial 1-year increase in remaining LE from 78.9 to increment the remaining LE at age 20 has already risen to 68.0 years.

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Table 2 | WTP for 1-year increases in remaining HLE (the Dorian Gray case) Age at which WTP is calculated (years) 0 20 40 60 80 R H R H R H R H R H First 242.0 216.3 377.0 328.5 472.7 429.7 570.8 536.9 692.5 653.8 Second 233.4 210.0 359.0 317.8 452.3 416.8 538.0 519.2 612.0 618.6 Third 224.1 203.8 341.0 307.6 432.6 404.6 513.4 503.7 588.7 598.8 Fourth 214.2 197.9 322.6 297.7 413.0 393.0 493.0 489.8 531.6 583.9 Fifth 203.7 192.1 303.8 288.3 393.1 381.9 474.0 477.1 Tenth 136.6 165.3 197.0 245.7 230.0 331.6

WTP for the first, second and further 1-year increases in remaining HLE at ages 0, 20, 40, 60 and 80 years. The HLE remaining at these ages in the baseline simulation is 68.5, 48.8, 30.4, 14.9 and 4.8 years. Values are given in US$1,000. Some values are missing because there is an upper limit to how much HLE can be extended through rectangularization or improvements in lifespan. H, improvements in healthspan T*; R, rectangularization.

Although 1-year increases in LE are convenient for presentational Slowing aging (the Peter Pan case). We now consider the WTP for simplicity, each additional year of LE requires ever-larger propor- slowing aging itself, which leads to simultaneous improvements in tional changes in mortality rates at older ages, as noted in ref. 17. health and mortality. We assume aging occurs through the accumu- Three results stand out from Table 1: the WTP for additional gains lation of biological damage, and that slowing aging lessens the pace in LE diminishes as LE rises, it is greatest at older ages, and is higher at which health and mortality deteriorate with age. In the extreme under rectangularization. WTP diminishes as LE rises because the case, where aging is not just slowed but eliminated, mortality and gains progressively accrue more in the future, which means they health become independent of age and the individual is ‘forever are discounted more and occur in years of poor health. The fact young’. We refer to this as the ‘Peter Pan’ case, after the play and that WTP increases with age is also partly due to discounting (the novel21 about a boy who never grows old. To allow for a slowdown in old experience the benefits of extra LE sooner than the young) but aging we multiply chronological age a by a constant δ. For δ = 1, bio- mainly because the probability of reaching older ages and benefit- logical damage accumulates at its current rate but the lower δ is, the ing from the gains is increasing with age itself. Rectangularization is more slowly aging occurs and the greater the gap between biological preferred because it concentrates increases in LE. and chronological age. The ‘forever young’ case is given by δ = 0. In contrast to the Struldbrugg and Dorian Gray cases, WTP now Compressing morbidity (the Dorian Gray case). We next hold LE consists of two components, one representing the gains in mortality fixed but improve the relationship between health and age. Under and the other representing gains in health. Table 3 shows the total this scenario, which we refer to as the Dorian Gray18 case, HLE rises WTP for slowing down aging to achieve 1-year step increases in LE. as a proportion of LE to create a ‘compression of morbidity’19. In the Compared to Struldbrugg, Peter Pan has higher WTP because now eponymous novel, Dorian Gray has a portrait painted and while the both health and LE are increasing. The WTP for further delays in picture ages, Gray himself does not, retaining his health and looks aging still declines but at a slower rate owing to the complemen- until he dies. Following ref. 20, we assume morbidity is also subject tarities between health and longevity; that is, the higher the LE, the to a compensating effect such that health declines to reach H* at greater the WTP for an increase in health, and the better the health, age T*. Under rectangularization, gains are reflected in better health the greater the WTP for improvements in LE. prior to T* but a faster deterioration around T*, whereas improve- As above, the WTP for improvements increases with age so that ments in healthspan stretch the health function so it reaches H* at the gains from slowing aging are greater for the old. According to higher values of T*. Table 3, the value of delaying aging rises as the average age of society The results (Table 2) indicate that the WTP for improvements in increases, leading to a shift in the diseases that the medical system HLE diminishes as HLE rises and also increases with age. As before, should focus on. This is consistent with the argument of a fourth this reflects a combination of discounting and the higher probabil- stage of Omran’s epidemiological transition (‘the age of delayed ity of older individuals reaching even older ages. However, an addi- degenerative diseases’)22,23. tional force is at work in this case because as health improves in later life, individuals respond by allocating more consumption and Reversing aging (the Wolverine case). A hypothetical alternative leisure to these years, and gains in health at older ages become more to the Peter Pan scenario is a reversal of aging, in which biological attractive. This also explains why extending healthspan is eventually damage is repaired rather than slowed. For our literary reference preferable to rectangularization. we turn to the Marvel character Wolverine24 and his daughter X-23, Tables 1 and 2 show that the economic value of gains from an who both possess a healing factor enabling body tissue to be regen- extra year of HLE always exceed those from an extra year of LE. An erated. Recent advances have shown that such regeneration is pos- increase in LE in the Struldbrugg case provides additional years sible in mice and humans25,26. in which to enjoy lifetime consumption and leisure, but declin- We capture this by assuming a one-time intervention at age 65 ing health makes this less appealing than the increase in health that rewinds an individual’s biological clock back to a specific age, Z. at each age under the Dorian Gray case. This preference for HLE Supplementary Table 1 reports the WTP for such a reversal in which over LE extends to preferring a full compression of morbidity. gains are once more by 1-year increases in LE; for example, in the Even though the WTP for additional years of HLE decreases with row starting ‘First’, WTP at 0 years is US$103,500 for a first reversal further 1-year increases in remaining HLE (Table 2), it never falls in aging at age 65 that increases LE at birth from 78.9 to 79.9 years. below the WTP for the first increase in LE in Table 1. Individuals Reversing aging sounds more dramatic than slowing aging, but always prefer an extra year of HLE to adding an additional year to the differences in our model are subtle. This is because we assume current US LE. that aging slows down over the entire adult life whereas a reversal

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There are two reasons to expect large gains when comparing met- Table 3 | WTP for 1-year increases in remaining LE (the Peter formin to single disease treatments. The first is the rising prevalence Pan case) of age-related comorbidities, which makes targeting aging valuable Age at which WTP is calculated (years) as the impact will be felt across multiple diseases (see ref. 29). The 0 20 40 60 80 second is synergies between diseases: reducing the incidence of any given disease has more impact on LE and health when the incidence First 178.7 262.6 333.9 378.5 380.2 of other diseases is also reduced (the competing risks argument30). Second 175.1 257.4 328.5 373.8 377.7 In many ways, treatments that target aging are more similar to drugs Third 171.5 252.2 323.1 369.2 375.0 that save lives at younger ages and promote longer spells of healthy life, rather than treatments aimed at extending lifespan for shorter Fourth 168.0 247.0 317.8 364.6 372.0 periods of time in poor health. Fifth 164.5 241.9 312.4 360.0 368.9 We make three assumptions regarding the age at which treat- Tenth 147.5 217.3 286.3 337.6 352.6 ment starts: 75 (the average age of participants in the study), 65 (all 28 Twentieth 116.9 172.6 236.1 293.1 319.1 participants are over 65) and 50 years. As ref. only includes men over the age of 65 with diabetes, the factors may not accurately Thirtieth 91.1 134.7 189.6 247.3 281.6 λa,i capture the impact of metformin on women, individuals who do WTP for the first, second and further 1-year increases in remaining LE at ages 0, 20, 40, 60 and not have diabetes, or those aged under 65. Metformin may also have 80 years. The LE remaining at these ages in the baseline simulation is 78.9, 59.0, 39.5, 21.7 and 8.4 31 years. Values are given in US$1,000. less of an impact at higher ages . The WTP calculations we present are broadly linear in the λa,i factors so it is relatively easy to scale the gains up or down. For example, if the impact for individuals without diabetes is only 10% of that for those with diabetes, then multiplying occurs only at age 65. For this reason, the WTP in the Peter Pan case the WTP by 0.1 gives an appropriate estimate of the gains. is greater than for the Wolverine case at younger ages and the WTP Based on ref. 28, metformin has a sizable effect on LE. For the case rises faster with age under the Wolverine case. This effect is further in which treatment starts at age 75, LE at birth rises by 2.9 years, at enhanced because reversal leads to a relative improvement of health 20 years rises by 3.0 years, at 40 years rises by 3.0 years, at 60 years at older ages, meaning that these years become more valuable as rises by 3.3 years, and at 80 years rises by 4.3 years. The additions to relatively more consumption is allocated to them. remaining HLE vary from 1.7 to 2.5 years. Supplementary Table 2 shows that the estimated benefits of met- Targeting aging versus single diseases. The results in the Peter Pan formin are substantial, often matching or exceeding those from and Wolverine cases suggest that the gains to slowing or reversing the complete eradication of cancer, dementia or cardiovascular aging are substantial. This raises two further questions. How much diseases. Figure 2 breaks down the WTP for metformin, starting can aging be realistically slowed? And how does the WTP for slow- at 75, by year of life in which the benefits occur. The total WTP ing aging compare to that for the reduction or eradication of specific for metformin significantly exceeds the sum of the separate effects diseases? In this section, we explore these questions with reference due to metformin’s beneficial impact on competing risks. The mag- to metformin, a drug prescribed for type 2 diabetes that is consid- nitude of these aggregation and complementarity effects increases ered to produce ‘protective effects against several age-related dis- with the number of diseases under consideration. Although Fig. 2 eases’27. We do so by utilizing the results of ref. 28 (based on a study focuses only on non-communicable diseases, extending the analy- of 41,204 men with diabetes with an average age of 75), which pro- sis to include infectious diseases such as Covid-19, whose mortality vides detailed year-by-year estimates of the effect of metformin on rises with age, will increase the estimates even further. the incidence of various age-related comorbidities. Two features of our focus on both metformin and the results of Aggregate gains. We now shift from calculating individual gains to ref. 28 should be emphasized. The first is that the efficacy of metfor- the total gains aggregated across all ages in society, as well as includ- min awaits confirmation from large sample trial data such as from ing the benefits to as yet unborn generations8. Focusing on the aggre- the Targeting Aging with Metformin (TAME) trial. Our calculated gate WTP reveals a powerful additional dynamic at work. Slowing results will naturally differ if such results lead to different estimates down aging leads to a population that is on average older and larger than in ref. 28. The second is that the key results of this section are (as more people live for longer), both of which increase the aggregate valid for any intervention, clinical or otherwise, that attenuates the WTP for further improvements. This creates a virtuous circle around effect of aging. For instance, education is widely seen to impact delaying aging; the better that society ages, the more valuable any health outcomes and could be considered in exactly the same way as further improvements. To calculate this aggregate WTP, we sum the metformin in our simulations. The case of education shows not just age-specific individual WTPs from the Peter Pan scenarios using the the relevance of non-clinical interventions but also that interven- latest US Census Bureau data on the population, its age structure and tions can occur across the life course. birth rates. For consistency, we measure improvements in terms of For our purposes, ref. 28 provides estimates of a set of factors step increases in LE achieved by adjusting the speed of aging. 0 ≤ λa,i ≤ 1 that measure the reduction in the incidence of disease Based on Table 3 (first row) and current census data, the total (i) after a year of treatment. Denoting the incidence of disease in the WTP for a 2017 slowdown in aging leading to a 1-year increase absence of metformin by πa,i and the same incidence when taking in LE is US$37.6 trillion (US$29.7 trillion for those alive in 2017, ∗ ∗ = = metformin by π the factors satisfy π λa,iπa,i. If λa,i 1 then US$7.9 trillion for those not yet born). The corresponding number a,i = a,i metformin has no effect and if λa,i 0 the disease is eradicated. In for a 10-year increase in LE is US$366.8 trillion (split US$291.9 tril- our case, the factors after 5 years of treatment are 0.52 for dementia, lion, US$74.8 trillion). Based on a 2% interest rate, the value of this 0.33 for cardiovascular diseases, 0.32 for cancer, 0.29 for depression 10-year increase is US$7.2 trillion at an annual rate (or 33.6% of and 0.58 for frailty-related diseases. We use the Global Burden of 2019 GDP). These calculations abstract from the diversity of health Disease dataset2 to identify the number of US deaths and years lost across the US population32,33, so they are likely to underestimate the to illness due to each of these age-related morbidities, and adjust aggregate gains from delaying aging. them downwards by the λa,i factors. The WTP for metformin con- The value of a further delay in aging in 2050 is shown in Table 4 sists of two components, representing gains to mortality and the (fourth to sixth row). These depend on the individual WTPs for health benefits arising from reduced incidence of disease. a second incremental slowing of aging (for example, Table 3,

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70 75 80 85 90 95 100105 Age (years)

Reduction in cancer Reduction in depression Reduction in dementia Sum of separate effects

Reduction in cardiovascular disease Total effect Reduction in frailty-related diseases

Fig. 2 | WTP by year of life for metformin treatment started at age 75. The value for each year (by age) of improvements in the incidence of various diseases under simulated impact of metformin. Sum of separate effects, the total of each individual effect; Total effect, the overall value for each year of health improvements attributed to metformin. Solid lines represent WTP for each of the five comorbidities separately.

Table 4 | Society WTP for successive slowdowns in aging Increase in remaining LE (years) 1 2 3 5 10 Society WTP for first slowdown in aging in 2017 Living population 29.7 59.3 88.8 147.4 291.9 Unborn generations 7.9 15.6 23.3 38.5 74.8 Total 37.6 75.0 112.1 185.9 366.8 Society WTP for second slowdown in aging in 2050 Living population 30.0 60.3 90.7 152.1 307.9 Unborn generations 6.8 13.5 20.1 32.9 62.4 Total change 36.9 73.8 110.8 185.0 370.3 Change in society WTP from 2017 to 2050 Change in individual WTP −0.05 −0.20 −0.50 −1.63 −8.82 Between first and second slowdown of aging Change in society WTP from 0.11 0.48 1.13 3.41 15.98 Increase in population due to slowdown of aging Change in society WTP from 0.26 0.69 1.29 2.92 8.77 Independent changes in population Change in society WTP of −1.03 −2.10 −3.23 −5.62 −12.47 Unborn generations Total change −0.70 −1.14 −1.31 −0.91 3.47 second row), as well as the 2050 projected population age structure. the second wave are worth slightly less (approximately 1–2%) but To obtain estimates of the latter, we start from the 2017 population for larger improvements slightly more (approximately 1%). Table 4 and forecast forward using current birth and mortality rates from provides a breakdown of the factors driving the change in the aggre- 2017, adjusted for the assumed initial improvement in aging and gate WTP. One reason that the aggregate WTP changes between setting net immigration to zero. the two rounds is due to changes in individual age-specific WTPs. The aggregate WTP for the 2017 and 2050 delays in aging are of As shown in Table 3, the WTP for further delays in aging declines similar magnitude. For smaller improvements in LE, the WTPs for at each age and this lowers the 2050 aggregate WTP. This effect is

620 Nature Aging | VOL 1 | July 2021 | 616–623 | www.nature.com/nataging NaTUre AgIng Analysis shown in the first line of the breakdown (Table 4), in which a 1-year increase in Table 4. Adjusting for differences in chosen discount rates increase in LE decreases the aggregate WTP by US$45.8 billion. and VSLs and restricting our gains to the over 50 s only leads to an The aggregate WTP also changes between the two waves of aging estimate of the aggregate gains as worth US$21 trillion. The remain- improvements because of changes in population. Independent of ing differences are attributable to ref. 29 assuming a phased rather the delays in aging that we model, there is expected to be an increase than immediate improvement in aging. Although differences remain, in the average age of the US population of 4.0 years between 2017 the most important insight is that their different approach (using and 2050 and (assuming zero net immigration) a decrease in popu- an empirical microsimulation model based on US individual data) lation size by 1.6 million people. The increase in average age boosts arrives at similar very large estimates for the value of delaying aging. the aggregate WTP (delaying aging is more valuable for the old) Our estimates abstract from both inequalities in health and while a shrinking population lowers it (aggregation occurs over income. Allowing for health inequalities is likely to increase the fewer people). The second row of the deconstruction shows that value of the aggregate gains, but introducing income inequality raises the aging effect dominates, so the combined impact is positive and important distributional issues. Our estimates suggest that treat- raises the aggregate WTP by US$113.7 billion in the case of a 1-year ments that target aging are extremely valuable. If the cost of such increase in LE. treatments is low then access to them will be widespread. If, how- Additional changes in the age structure are induced by the ever, the costs are high then issues of access and redistribution will assumed delay in aging. This leads to more people alive at older become important. What is clear from the magnitude of the poten- ages and in better health in 2050, raising the aggregate WTP. tial values outlined in our simulations is the need to ensure wide- Table 4, third row, shows that this is worth US$256.7 billion for the spread access if the full value of these social gains is to be realized. case of a 1-year in crease in LE and US$8.8 trillion for a 10-year increase in LE. Importantly, the size of this channel increases faster than the gains to LE. Improvements in LE have a dispro- Methods Economic model. At the heart of our model is lifetime expected utility from the portionate impact on the size and age of the older population, so perspective of age a, given by this induced population change increases rapidly in response to ∞ ∫ ∗ − ( − ) improvements in aging. It is this that produces the virtuous circle H(t)u(c(t),l(t))S (t, a)e ρ t a dt through aggregation. a where H(t) denotes health at age t, ( ( ) ( )) the utility function (which depends For small improvements in LE, the negative effects of declin- u c ∗t ,l t ing individual WTP and fewer births are greater than the positive on consumption c(t) and leisure l(t)), S (t, a) is the survival rate from age a to t, and ρ is the subjective discount rate determining the weight individuals give to effects from changes in population structure. As a consequence, the the future. As shown previously8, assuming an optimizing agent gives the value of ′ ′ aggregate value of gains to aging declines. Closer examination sug- a life year at age t as ( )= ( )( − ( )) − ( )+ ( ( ) ( )) , where v t w t T l t c t ′ u c t ,l t /uc gests that this virtuous circle remains true even for the case of small w(t) is the wage rate, T – l(t) is working hours and uc is the marginal utility of gains in aging. Focusing on the two factors that are endogenous to consumption, ∂u(.)/∂c. The value of a life year therefore depends on two items: a term reflecting the our model (changes in the individual WTP and induced popula- ′ ′ ( ( ) ( )) value of utility gained that period from consumption and leisure, u c t ,l t /uc; tion changes) reveals their sum to be always positive, reflecting an and a term reflecting savings. Years in which savings are positive are given a aggregate virtuous circle. higher value as they provide financing for consumption at other points in life. An The second reason that the virtuous circle exists for even small important feature of this model is that the value of life is substantially higher than delays in aging is connected to whether the WTP for gains to LE the value of income earned over a life. That is because leisure itself has a value are really declining at the individual level. Throughout, we have and the wage at any age provides a way to value this, even if an individual is not working. focused on measuring improvements in health, longevity and aging Using this approach, the value of life at age a is ∞ − − ∗ by focusing on 1-year step increases in LE. However, one reason ( )=∫ ( ) r(t a) ( ) , where r is the real return the individual V a a v t e S t, a dt that the individual WTPs for Peter Pan decline in response to fur- earns on their assets. Based on this formula8, we show that WTP at age a for ther delays in aging is that each 1-year increase in LE represents a improvements in longevity in response to changes in medical knowledge (ζ) is ∞ smaller percentage increase in LE and larger proportional changes ∫ ∂ log S(t, a) in mortality rates. If instead we focus on percentage improvements v (t) S(t, a) , a ∂ζ in aging (for example, a 1% slowdown in biological aging rather than a slowdown generating a 1-year increase in LE) then we have while the WTP for improvements in health is ′ increasing WTP at an individual level. In other words, measurement ∞ ( ) ∫ Hς t u(c(t),l(t)) ′ S(t, a)dt, of aging biologically rather than chronologically leads to increasing H(t) u returns for aging at the individual level, feeding into even greater a c ∗ ( − ) increasing returns at the aggregate level. where S(t, a)=S (t, a)er a t , the discounted survival function. Following ref. 8, we assume that utility depends on a composite z of η − 1 − 1 − [ 1 − 1 ] η 1 Conclusion consumption and leisure such that z = ϕc η +(1 ϕ) l η , where The economic value of gains from targeting aging are large because η denotes the elasticity of substitution between consumption and leisure, the delaying aging produces complementarities between health and willingness of the individual to trade off consumption against leisure34. The utility longevity, affect a large number of diseases due to the rising preva- function is lence of age-related comorbidities, and create synergies arising from − − z1 1/σ − z1 1/σ competing risks. Crucially, delaying aging leads to a virtuous circle u (z)= 0 , 1 − 1/σ in which slowing aging begets demand for further slowing in aging. 35 This virtuous circle arises because society’s gains from delaying where z0 (as in ref. ) is a normalization capturing an individual’s attitude towards life versus non-existence. The parameter σ is the intertemporal elasticity of aging rise with the average age of society, increase with the qual- substitution (IES) that plays a key role in the model as it captures the willingness of ity of life in old age, and depend on the number of older people. the individual to reallocate consumption across time periods. The higher the IES This provides a distinctive dynamic to targeting aging compared to the more an individual is concerned about total life consumption, and the lower the treatments aimed at specific diseases, in which gains diminish once IES the more they are concerned about per-period consumption. successful treatments are discovered. Our model follows a three-stage life, of childhood and education, work 29 and then retirement. We assume that adulthood begins at age 20 and that Our estimates are larger than those in ref. , which calculates consumption during childhood is financed by parents. We assume an initial a slowdown in aging producing a 2.2-year increase in LE as worth wage that is constant between 20 and 25 years and then starts to rise with age US$7.1 trillion to those aged over 51. This case is closest to our 2-year such that w(a)/w (20)=γ log a until retirement at a = R, with γ reflecting the

Nature Aging | VOL 1 | July 2021 | 616–623 | www.nature.com/nataging 621 Analysis NaTUre AgIng degree to which wages rise with experience. For a > R we set wages equal to Reporting Summary. Further information on research design is available in the w (a)=Ψ (a) w(R). In the case in which Ψ (a)=1, the wage post retirement Nature Research Reporting Summary linked to this article. is equal to the retirement value and does not decline (consistent with a previous model36). The case of Ψ (a) < 1,a>R is consistent with previous studies37,38 and 36 Data availability we allow for this with the interpretation offered by ref. that the discount reflects a The data for the incidence of disease were taken from the Global Burden of Disease shift to part time work paying a lower salary. The post-retirement wage falls in line dataset (http://ghdx.healthdata.org/gbd-2019). The US population Census data were with health with elasticity ξ. taken from https://www.census.gov/programs-surveys/popproj/data/datasets.html. Health and mortality. We use a Gompertz equation for mortality, in which imposing a compensating effect of mortality gives the restricted expression Code availability ( − ) μ (a)=Meβ a T . We set T = 97.6 and M = 0.3319 based on cross-country All simulations were performed using MATLAB version 9.6.0.1072779 (R2019a). evidence39, and then calibrate β = 0.0966 so that LE at birth matches that in the US All codes are available upon request. for 2018 (78.9 years). For health we follow refs. 13,40 and assume at age a that an individual Received: 8 January 2021; Accepted: 19 May 2021; −μa has disabilities given by D (a)=E + B and health at age a is Published online: 5 July 2021 H (a)=[D(0)/D(a)]α. We impose a compensating effect of morbidity using the ∗ − ∗ ( − ) restriction B = D e μT so that D (a)=E + D eμ a T . For calibration purposes we use the results of previous studies20,41: E = 0.0821, B = exp(−0.504), α = 0.34. References We choose µ to match∞ US HLE in 2018 of 68.5 years (World Bank data), where 1. Oeppen, J. & Vaupel, J. W. Broken limits to life expectancy. Science 296, ∗ HLE is defined by ∫ H (t) S (t, a) dt. 1029–1031 (2002). 0 For Peter Pan we assume that aging is captured by a frailty index F (a)=θeδa 2. GBD 2019 Demographic Collaborators. Global age-sex-specifc fertility, ∗ ∗ ( − ) mortality, healthy life expectancy (HALE), and population estimates in 204 and impose a compensating effect such that = δT so that ( )= δ a T θ F e F a F e countries and territories, 1950–2019: a comprehensive demographic analysis . We assume that the disability index is given by ( )= + ( )ψ and ∗ D a E BF a for the global burden of disease study 2019. Lancet 396, 1160–1203 (2020). ( )= ( )λ mortality by μ a M F a , pinning down a relationship between our earlier 3. Olshansky, S. J. 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31. Espada, L. et al. Loss of metabolic plasticity underlies metformin toxicity in References to metformin and associated literature were researched by D.A.S. A.J.S. led aged Caenorhabditis elegans. Nat. Metab. 2, 1316–1331 (2020). the writing of the manuscript, which was edited by all authors. M.E. led the coding and 32. Cantu, P. A., Hayward, M. D., Hummer, R. A. & Chiu, C.-T. New estimates of model solution. racial/ethnic diferences in life expectancy with chronic morbidity and functional loss: evidence from the National Health Interview Survey. J. Cross Competing interests Cult. Geront. 28, 283–297 (2013). A.J.S. is a co-founder of The Longevity Forum, an advisor to Genflow BioSciences, has 33. Garcia, M. A. et al. Educational benefts and cognitive health life acted as a consultant for GlaxoSmithKline and the United Nations on issues of longevity expectancies: racial/ethnic, nativity, and gender disparities. Gerontologist 61, and is a member of the World Economic Forum’s Healthy Ageing and Longevity Global 330–340 (2020). Future Council. M.E. has no competing interests. D.A.S. is a consultant, board member, 34. Dotsey, M., Li, W. & Yang, F. Consumption and time use over the life cycle. equity owner and inventor on patents at EdenRoc companies (including MetroBiotech, Int. Economic Rev. 55, 665–692 (2014). ArcBio, Dovetail Genomics), Life Biosciences (including Iduna, Continuum, Sephagy), 35. Rosen, S. Te value of changes in life expectancy. J. Risk Uncertain. 1, Cohbar, Alterity, Catalio Partners, TB12, InsideTracker, Immetas, NDLX and Frontier 285–304 (1988). Acquisition. D.A.S. is an advisor to Zymo Research. Details and additional disclosures 36. Casanova, M. Wage and earnings profles at older ages (Univ. Chicago, 2012). can be found at https://sinclair.hms.harvard.edu/david-sinclairs-affiliations. 37. Hanoch, G. & Honig, M. ”True” age profles of earnings: adjusting for censoring and for period and cohort efects. Rev. Econ. Stat. 67, 383–394 (1985). Additional information 38. Johnson, R. W. & Neumark, D. Wage declines among older men. Rev. Econ. Supplementary information The online version contains supplementary material Stat. 78, 740–748 (1996). available at https://doi.org/10.1038/s43587-021-00080-0. 39. Milevsky, M. A. Calibrating Gompertz in reverse: what is your longevity-risk- Correspondence and requests for materials should be addressed to A.J.S. adjusted global age? Insurance: Math. Econ. 92, 147–161 (2020). 40. Finkelstein, A., Luttmer, E. F. P. & Notowidigdo, M. J. What good is wealth Reprints and permissions information is available at www.nature.com/reprints. without health? the efect of health on the marginal utility of consumption. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in J. Eur. Economic Assoc. 11, 221–258 (2013). published maps and institutional affiliations. 41. Strulik, H. Te health hump. J. Demographic Econ. 83, 245–258 (2017). Peer review Information Nature Aging thanks S. Jay Olshansky, John Rowe and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Acknowledgements Open Access This article is licensed under a Creative Commons We are grateful to A. de Grey for insight and suggestions regarding modelling frailty Attribution 4.0 International License, which permits use, sharing, adap- and age reversal, and to C.-P. Wang for providing data on the impact of metformin. J. M. tation, distribution and reproduction in any medium or format, as long Aburto, K. Ellison and E. Verdin provided useful comments. Y. Cao, A. Groom and D. as you give appropriate credit to the original author(s) and the source, provide a link to Hein provided valuable research assistance. We acknowledge funding from the Economic the Creative Commons license, and indicate if changes were made. The images or other and Social Research Council (ESRC, grant T002204) to A.J.S., the John Fell Fund to M.E., third party material in this article are included in the article’s Creative Commons license, and from the Glenn Foundation for Medical Research to D.A.S. unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statu- Author contributions tory regulation or exceeds the permitted use, you will need to obtain permission directly The original idea for the paper emerged from a conversation between A.J.S. and D.A.S. from the copyright holder. To view a copy of this license, visit http://creativecommons. Discussions on how to model these issues economically, how to structure the various org/licenses/by/4.0/. models and the economic interpretation of results were taken jointly by M.E. and A.J.S. © The Author(s) 2021

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